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### Course: 6th grade>Unit 11

Lesson 7: Box plots

# Constructing a box plot

Here's a word problem that's perfectly suited for a box and whiskers plot to help analyze data. Let's construct one together, shall we?. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• If the number of samples is even and we have to take the median using the 2 middle numbers instead of 1, do you not use both of those middle numbers when you go to find the 25th and 75th quartiles too?
• You add up the two middle numbers and then divide them by two (average).
• How do you find range?
• Range is found by subtracting the lowest value in a data set from the highest value. So if the values in the data set were {4,8,9,16,22,30} you would find the range by calculating 30 - 4 = 26. 26 is the range.
• Ugh! I still can't understand it, even though I watched this amazing video! Could someone explain it to me in a nutshell? I just don't get how you make the graph! Also, maybe someone could recommend a Khan video that can help me. Thanks in advance!
• I am also not very good at explaining, and I hope this isn't too late to answer your question, but this video is mainly about the characteristics and details of a box and whisker plot. Sal demonstrates when to use a box plot in the beginning of the video and to use it to see the median and all of the values. He then tells us to arrange all the numbers so we can find the median of the data set, as to create the box and whisker plot. When you have figured out the median, you would separate the numbers in halves and like Sal said, if there is an even number of values, you have to find the average of the middle two numbers. These apply to find the first and third quartiles of the data set. In a box plot, you use the minimum, the first quartile value, the median, the third quartile value and the maximum value. If you still don't get it here is a helpful link :
http://www.wikihow.com/Make-a-Box-and-Whisker-Plot
If this is too complicated, don't mind the info about outliers. :)
• I don't understand Box and whisker plots still
• So the box and whiskers plot is composed of five data points. It is the summary of your distribution. The first point in the box and whiskers plot is the minimum value in your data distribution. The second point is the Q1 value (the value to which 25 percent of the data fall to the left). The third point is the median of your distribution. The fourth point is your Q3 value (the value to which 75 percent of the data fall to the left). The last point is the maximum value in your data distribution. The box and whiskers plot is summary of our data and often can be used to identify low and high outliers. For instance, to find a low outlier, we can use the equation: Q1 - 1.5 (Q3-Q1). To find a high outlier, we can use the equation: Q3 + 1.5 (Q3-Q1). By the way, the (Q3-Q1) is called the IQR and it is a measurement of the spread of your data. Hope this helps :)
• what is meadian
• The median is a type of average, in which we find the middle term having first placed the terms in numerical order.
• Hello don't have a good day have a great day!
• bruh seriously?
• What's the interquartile range??
• The interquartile range is defined as the 75 percentile minus the 25 percentile.

Have a blessed, wonderful day!
• does the summer have to start at zero??
• Nope! You could have a number line that starts at 183, or -5248.
• This is just a summary of everything Sal is doing, just in case you are confused.

1) order data points from least to greatest -- all the numbers are ordered at

2) find the median of all the numbers -- the circled number at is the median

3) find the median of ONLY the bottom half -- so take all the numbers below the original median that we found, and take the median of those numbers, shown at

4) find the median of ONLY the top half -- ie do the same you did in step 3, except for all the numbers above the median, the circled dark pink number at is the top median

5) graph -- the whisker in the front starts at the smallest number in the ordered numbers, in this case, 1. The whisker in the back ends at the biggest number in the ordered numbers, in this case, 22. The bottom edge of the box is at the lowest median (ie what we found in step 3). That is where you stop the lower whisker. The middle line in the box is at the median of all the numbers (ie what we found in step 2). The top edge of the box is at the highest median (ie what we found in step 4). The highest median is where you start the top whisker.

Hope this helps!